The weak Galerkin (WG) finite element method is an effective and robust numerical technique for the approximate solution of partial differential equations. The essence of the method is the use of weak finite element functions and their weak derivatives computed with a framework that mimics the distribution or generalized functions. Weak functions and their weak derivatives can be constructed by using polynomials of arbitrary degrees; each chosen combination of polynomial subspaces generates a particular set of weak Galerkin finite elements in application to PDE solving. This article explores the computational performance of various weak Galerkin finite elements in terms of stability, convergence, and supercloseness when applied to the model Dirichlet boundary value problem for a second order elliptic equation. The numerical results are illustrated in 31 tables, which serve two purposes: (1) they provide detailed and specific guidance on the numerical performance of a large class of WG elements, and (2) the information shown in the tables may open new research projects for interested researchers as they interpret the results from their own perspectives.